Large deviations of Gaussian tandem queues and resulting performance formulae

This paper considers a two-node tandem queue where the cumulative input traffic is modeled as a Gaussian process with stationary increments. By applying (the generalized version of) Schilder's sample-path large-deviations theorem, we derive the many-sources asymptotics of the overflow probabilities in the second queue; `Schilder' reduces this problem into finding the most probable path along which the second queue reaches overflow. The general form of these paths is described by recently obtained results on infinite intersections in Gaussian processes; for the special cases of fractional Brownian motion and integrated Ornstein-Uhlenbeck input, they can be explicitly determined, as well as the corresponding exponential decay rate. As the computation of this decay rate is numerically involved, we introduce an explicit approximation (`rough full-link approximation'). Based on this approximation, we propose performance formulae that could be used, for instance, for network provisioning purposes. Simulation is used to assess the accuracy of the formulae